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At experimental equilibrium volume, the total energy of CaTiO〓 increased with the displacement of Ti along [001] direction and the lowest energy point is always at zero displacement of Ti. However, with a 10% volume expansion, the displacement of Ti along [001] direction results in a shallow, but well-defined double energy well and ferroelectricity appears.

钛酸钙在实验晶胞体积下，钛离子沿[001]方向的位移不会引起总能量的降低，当体积膨胀10％时，钛离子的位移会引起系统的总能量的降低，在一定的位移时总能量呈现极小值，即出现铁电性。

Three displacement functions w,Gand ψare introduced in this paper tosimplify motion equations of elasticity problenis in spherically isotropic media to an indepen-dent partial differential equation concerning one displacement function ψand simultaneous equations concerning two other displacement functions w and G.

本文引入三个位移函数，将球面各向同性弹性力学运动方程，简化为关于ψ的二阶偏微分方程，和关于W和G的联立方程。在静力学问题中，联立方程可进一步简化，w和G可用另一位移函数F表示，而F满足一个四阶偏微分方程。

In this paper, the sine and cosine shaped sensors have been designed by using the integral characteristics of PVDF piezoelectric film. The sine PVDF sensor can be used alone to measure the displacement, speed, acceleration, stain, stress of the roof beam vibration; the cosine PVDF sensor can be used alone to measure the angular displacement and shear of the roof beam vibration; by using them jointly , the structural intensity can be measured for the roof beam without any finite differential error.

本文利用PVDF压电薄膜独特的积分特性，设计制作了正弦形状和余弦形状传感器，它们单独使用，正弦形状的PVDF传感器可以用来测量梁振动的位移、速度、加速度、应变、应力、弯矩；余弦形状的PVDF传感器可以测量振动梁的角位移和剪力；配对使用它们，可以用来测量梁的结构声强，用它们测量结构声强时不会产生有限差分误差。

PICC is of higher performance than PLC, it can more easily solve the problem of sampling bed thickness and the control of electro-magnetic valves and so on in jig automation, buoyage displacement sensor can be sublimated to a complex sensor by means of the dynamic analyze of buoyage displacement signal.

可编程智能卡在过程控制中具有比PLC优越的性能，在跳汰自动化的应用中可更方便地实现床层厚度的采样与电磁风阀控制等工作，通过对浮标位移信号的动态分析可将浮标位移传感器升华为一个可感知多个参数的复合传感器。

Crown gear coupling can compensate the radial and axial displacement and angular displacement between axes. Its structure is compact. It can transmit motion reliably and accurately and avoid the stress concentration in sharp corner of teeth. So this coupling's carrying power is large.

具有补偿轴线间相对径向位移、轴向位移和角位移的能力，并且结构紧凑，传递运动准确、可靠，能有效地避免齿的尖角应力集中，具有较大的承载能力。

Results show that gas release in gassy sand will cause the additive deformation of tunnel and additive stress of the shield segment, and make important impacts on the global displacement of tunnel but little influences on the stress of shield segments and the relative displacement of tunnel. It is inclined to arouse the differential settlement and cracks on the tunnel so as to cause hazardousness. Re-accumulating of the gas can also produce additional stress and the additive resilience, but it can be ignored in practical engineering because the influence degree is small. The shallow gas in reservoirs is appropriate to be discharged before construction of the subway tunnel.

研究结果表明：气体释放将引起隧道产生附加变形和管片附加应力，浅层气体释放对地铁隧道结构应力和结构相对变形影响较小，而对隧道整体位移影响较大，易引起不均匀沉降，导致隧道裂缝或断裂，进而引发危险；气体重新回聚时，隧道产生的附加应力和回弹位移量较小，工程中可不予考虑；地铁隧道施工前，宜对浅层气体进行预先排放。

Since the lengths of the line segments and the angles between line segments are treated as representation parameters, it is convenient to construct energy function and to deal with displacement and length constraints. Based on this advantage, a parametrical model for human body is proposed, which can easily produce human body models with different feature sizes. The above method is just suitable for polylines. Therefore, a generic deformation method for both discrete curves and surfaces is presented. The energy function is constructed by analyzing the relationship of the points before and after deformation. Together with the displacement constraints, the deformation problem is converted to a convex quadratic programming. A necessary condition for constraint points and a sufficient condition for the uniqueness of solution are given. The proposed method can be combined with skeleton-driven animation to control the deformation.

将线段长度与线段之间的角度作为表示参数，既有利于能量函数的构造，又便于处理位移约束和长度内蕴约束条件，利用这一优势，将其应用于三维人体的参数化建模，可以方便地产生具有不同特征尺寸参数的人体模型，由于这种方法只适用于折线变形，具有较大局限性，因此，本文进一步提出一种较通用的离散曲线曲面变形方法，通过分析变形前后的位置关系来构造能量函数，再加上位移约束条件，将变形问题转化为一个凸二次规划问题，并且给出了约束点应满足的必要条件及模型解唯一的充分条件，这种方法还可以与骨架驱动变形的思想相结合，能更好的控制变形。

To meet requirement of production and quicken rolling speed, No.2 heating furnace was put into operation in 2002 and No.3 in 2007. All automatic control was adopted, displacement of walking beam was detected by displacement transducer, and acceleration and deceleration control of walking beam was carried out through proportional valve and by use of slope technique in program of GE 90-70 PLC, thus, travelling speed of walking beam can be controlled and lift and release of slab can be operated lightly.

为适应生产的需要，加快轧制速度，2002年投产的2号加热炉和2007年投产的3号加热炉均采用全自动控制，利用位移传感器检测步进梁的位移量，通过比例阀以及在GE90-70PLC程序中采用斜坡技术对步进梁运动进行加减速控制，达到控制步进梁运行速度的目的，实现对板坯的轻拿轻放。

Base on the invariableness of lyapunov exponent, one can establish displacement forecast model, so intending slope displacement can be calculated through this model.

利用该指数的不变性就可以建立位移预测模型，这样就可以对边坡未来的位移变化做出预测。

In studies of interaction among pile, platform that above it and surrounding soil, this paper employ the concept of plate element to simulate the loading character of platform, and employ the concept of solid element to simulate the character of pile and soil, using the finite element method after understanding the geometry properties of pile, soil and the platform. Analyzing the loading properties of the three entities above and their deformation, this paper also employ a special element, Penalty Element. The introduction of penalty element of this kind has served to guarantee the join harmony of displacement between solid element and plate element, thereby effectively resolving the join problem between platforms, pile that support it and surrounding soil.Considering significant property difference between pile material and its surrounding soil, there may be much shear stress on their contact interface produced under vertical load, thus causing displacement or fission. Therefore it is necessary to adopt one special constitutive law of this kind of contact interface, which can reflect its feature of loading and deformation thoroughly. On the basis of the deformation feature and constitutive laws of some contact interface obtained by Zhang Dongji and people concerned through some single-shear experiments on contact interface between structure and soil, this paper employ one pile-soil three-dimensional constant thickness contact interface model to simulate the " slide" taken place on the interface between pile and its surrounding soil. With this kind model, this paper has also created one finite element model, which can be applied to perform finite element calculation and analyze the pile-loading feature, and deduced its element stiffness matrix.

在承台-桩-土共同作用中，考虑桩与承台的几何特性，采用有限元方法，用实体单元模拟桩土，用板单元模拟承台，更具体地分析桩和承台的受力特性和变形，而且还采用罚单元—既实体单元与板单元之间连接必须满足变形协调条件，来有效地解决了承台与桩土的连接问题，且在桩土共同作用中，由于桩体结构的材料性能与周围土层性质相差较大，在竖向荷载下有可能在其接触面上产生较大的剪应力从而导致错动或开裂，因此，为了充分反映桩土接触面上的受力及变形特征，应采用一种桩土接触面特有的本构关系，即利用张冬霁等人关于结构与土体接触面单剪试验所得到的接触面变形特征及其本构关系，引入桩-土三维等厚度接触单元来模拟桩与桩侧土之间的&滑移&，在此基础上建立可用于桩基承载性状分析的有限元计算单元模型，并推导出了各单元的刚度矩阵。

Liapunov—Schmidt method is one of the most important method in the bifurcation theory.

Liapunov—Schmidt方法是分叉理论的最重要方法之一。

Be courteous -- even when people are most discourteous to you .

要有礼貌──即使当別人对你最不礼貌的时候。